Interacting Binaries with Eccentric Orbits. Secular Orbital Evolution Due To Conservative Mass Transfer

TL;DR

This paper models the long-term orbital changes in eccentric binary systems caused by conservative mass transfer, revealing that such transfer can both increase and decrease orbital parameters over timescales from millions to billions of years.

Contribution

It introduces a formalism for secular orbital evolution due to mass transfer in eccentric binaries, accounting for both increases and decreases in orbital elements.

Findings

Mass transfer rates at periastron significantly affect orbital evolution.

Orbital parameters can both grow and shrink over time due to mass transfer.

Timescales vary from a few million to over a Hubble time depending on system parameters.

Abstract

We investigate the secular evolution of the orbital semi-major axis and eccentricity due to mass transfer in eccentric binaries, assuming conservation of total system mass and orbital angular momentum. Assuming a delta function mass transfer rate centered at periastron, we find rates of secular change of the orbital semi-major axis and eccentricity which are linearly proportional to the magnitude of the mass transfer rate at periastron. The rates can be positive as well as negative, so that the semi-major axis and eccentricity can increase as well as decrease in time. Adopting a delta-function mass-transfer rate of $10^{-9} M_\sun {\rm yr}^{-1}$ at periastron yields orbital evolution timescales ranging from a few Myr to a Hubble time or more, depending on the binary mass ratio and orbital eccentricity. Comparison with orbital evolution timescales due to dissipative tides furthermore shows that tides cannot, in all cases, circularize the orbit rapidly enough to justify the often adopted assumption of instantaneous circularization at the onset of mass transfer. The formalism presented can be incorporated in binary evolution and population synthesis codes to create a self-consistent treatment of mass transfer in eccentric binaries.